Nonlocal four-body interactions with non-trivial topological properties in a one-dimensional system of ultracold bosons

We present an effective theory of ultracold bosons in one dimensions with nonlocal four-body interactions and non-trivial topological properties. The effective interactions behave as a global (and scale-free) interaction between four particles that only turns on when separated pairs of particles come into contact. In the hard-core limit, the interaction creates a topologically non-trivial defect in configuration space, leading to multivalued wavefunctions with anyonic exchange statistics. It is one of only three possible few-body interactions with this property; the other two are local two-body interactions in two dimensions, leading to anyons with braid group statistics, and the local three-body interaction in one dimension, leading to anyons with traid group statistics. The nonlocal four-body interaction investigated here, which can be mapped to a system with two-body interactions in two dimensions, has conformal symmetry for any value of coupling strength leading to the possibility of probing spontaneous symmetry breaking of scale invariance. We analyze the model to identify spectral and dynamical signatures generated by the nonlocal interactions, anionic exchange statistics, and breaking of conformal symmetry.